We are a masjid that does not have a curtain, according to the sunnah.

A few people are insisting that we put a curtain. Part of their argument
is that Umar (ra) banned women from the mosque, so we should put a
curtain.

...
Did Umar ban women from the mosque?

I know of a hadith in Sahih Muslim where Umar's grandson (Bilal) wanted
to prevent women from coming to the mosque but Umar's son (Abdullah)
told him he could not go against the Sunnah of the Prophet.

Wa `alaykum as-Salam Sister Kathy:

Regarding the question: Did the Commander of the Believers `Umar ibn
al-Khattab - Allah be well-pleased with him - prevent women from attending
the mosque? The answer is: Yes, but only those who stayed there for
loitering/relaxation (istirwah), not those attending fard Salat.

Khawla bint Qays said: "We were women, in the Mosque [in Madina
al-Munawwara], who may have mixed with the men at times and perhaps even
flirted (ghazalna) and even harmed themselves in this intermixing; so
`Umar said: 'I swear I shall make free women of you again.' So he brought
us out (akhrajana) of the Mosque." Kanz al-`Ummal #23131 from Ibn Sa`d's
Tabaqat.

`Umar (RA) never prevented nor forbade women from attending the mosque for
the five obligatory prayers nor Tarawih.

This general permission and conditional prohibition is how he understood
the meaning of the hadith of the Prophet : "Do not forbid the
bondswomen of Allah from [going to] the mosques of Allah."

It is also related that he allowed them to pray Tarawih prayers in the
Mosque at Madina far from the men and ordered Sulayman ibn Abi Hatma to be
Imam for them, at the far end of the Mosque. Al-Muhalla (3:139).

In fact `Umar himself narrated that the Prophet said more
explicitly, "If your women ask permission to go out to Salat, do not
forbid them!" Musnad Ahmad (1:40).

To that end `Umar made sure they had a separate entrance and exit to the
Mosque, which he forbade men from using, and separate ablution facilities.
Al-Muhalla (3:131 and 4:119).

Yes, `Umar *disliked* for women to go the mosque.

`Atika bint Zayd the wife of `Umar would ask `Umar permission to go to
Salat in the Masjid and he would remain silent. She would continue, "I
swear I will go out unless you forbid me." She used to go out for Salat
al-`Isha and Salat al-Fajr. She was asked once: "Why do you go out like
that, knowing how jealous he is?" She replied: "And what prevents him from
forbidding us?" Musannaf Ibn Abi Shayba (1:106).

`Umar once said to her: "I swear that you know very well I dislike it."
She said: "By Allah! I shall not stop until you forbid me." `Umar replied:
"I truly do not forbid you." And the day `Umar was stabbed to death in the
mosque, she was present. Al-Muhalla of Ibn Hazm (3:139).

It is `A'isha - Allah be well-pleased with her - that tended to forbid the
women from going to the mosques, including for the five prescribed prayers
let alone Tarawih. She gave her reason in the famous statement: "If the
Messenger of Allah had seen what the women of our time do, he would have
forbidden them to go to the mosques just as the Israelite women were
forbidden." Sahih al-Bukhari, Sahih Muslim, and the books of Sunan.

The majority of the Ulema if not their Consensus agree - and Allah knows
best - that if women go to mosques - for obligatory prayers or otherwise -
then there should be (1) a separate entrance for them and (2) space for
prayer and facilities they can use in isolation from mixing with and view
by the men. And Allah knows best.

In conclusion: You are right that in the time of the Prophet there
was no curtain separating men from women. The men prayed directly behind
the Prophet , then the boys, then the women starting behind the last
row of the boys. But not having a curtain in the mosque today in not a
sunna in the sense of "something not obligatory but carrying reward, the
leaving which does not constitute sin."

Furthermore, the curtain is not against the Sunna but on the contrary is a
way to prevent fitna, which prevention is fard and a pre-requisite of
obligatory and recommended practices. There is a basic principle that "the
prevention of evil take precedence over the obtainment of good." Such
prevention, in other words, applies before everything.

In view of this, the Prophet said that the best place for a woman's
Salat is in the privacy of her house, and in another narration: in the
privacy of her room. If something approaching the function and purposes of
this private space can be reduplicated in the mosque, it should be welcome
as something close to Wajib, not fought.

So the curtain should be accepted, allowing men and women to pray on
alternate sides if space does not allow front rows for men and back rows
for women, which is a better arrangement. Together with this there should
be separate facilities and, if possible, separate entrances.

This conclusion reunites the basic stipulations of the texts on the issue
of women praying in the Mosque, not on the allegation that "`Umar banned
women from the mosque" but in order that believing men and women can
obtain the benefits of Jama`a without Shaytan interfering with them.
Wallahu a`lam.